High-Performance Constant-Time Discrete Gaussian Sampling

Abstract

Discrete Gaussian distribution plays an essential role in lattice cryptography whereas naive implementations suffer from timing attacks. Unfortunately, conversion to secure constant-time variant incurs severe deterioration in performance. In Knuth-Yao sampling, we demonstrate several properties of the discrete distribution generation tree involving structural features and finite node height. Accordingly we propose a generic method independent of standard deviations, which focuses on minimizing the Boolean expressions for the mapping from input bit strings to output sample values, along with an in-depth efficiency analysis. Two optimization techniques are devised to further propel the minimization by replacing and adjusting nodes. To strike the balance of computational overhead and closeness to optimum, heuristic strategies are introduced. Finally, performance evaluation is conducted both in software and hardware. Running on a 3.4GHz Intel Core i7-6700 processor, our method improves sampling rate by up to 29.5 percent compared to the latest technique. Targeting hardware FPGA devices, our approach can be 2.7 times faster and achieves 57.3 percent resource reduction than the original constant-time Knuth-Yao sampling. Compared to the Cumulative Distribution Table algorithm with fixed step binary search, our sampler can be at least 12.6 times faster and gains 79/61 percent better area-time product than its counterpart without/with BRAM.